PSI - Issue 23

Jiaming Wang et al. / Procedia Structural Integrity 23 (2019) 167–172 J. Wang et al. / Structural Integrity Procedia 00 (2019) 000–000

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and re-arragement of its constituents. The latter representation is used here. In addition to these meso-constituents, it is known that aggregates are coated with higher-porosity mortar with distinct properties, which is referred to as inter facial transition zones (ITZ) with typical thickness between 10 and 100 µ m [1, 2]. Having lower sti ff ness and strength than mortar, ITZ provide both preferable locations for damage initiation and easier pathways for crack development. The physical ITZ thickness is negligible in comparison with coarse aggregates, which makes ITZ models with phys ical thickness computationally demanding, sometimes prohibitively. This is presently tackled by representing ITZ as zero-thickness interfaces between aggregates and mortar, modelled computationally by cohesive elements [3–7]. Key parameters of ITZ cohesive laws, such as sti ff ness, critical strength and fracture energy, in both normal and shear directions, cannot be determined readily with existing experimental techniques. Therefore a combination of judgment as to how these di ff er from the mortar and parametric studies is used for their calibration. Selection of appropriate pa rameters is made by comparisons with experimentally observed macroscopic behaviour, including stress-strain curves and crack patterns. Previous works have demonstrated calibration of cohesive laws with experiments in either tension [3–6] or compression [7]. However, there is no work demonstrating the performance of calibrated cohesive laws un der both tension and compression, which is an essential condition for using this type of meso-structure models under complex stress states existing in real engineering structures. One critical element of the meso-structure - elastic aggre gates, plastic-damage mortar, cohesive ITZ - is the very distinct behaviour of mortar under tension and compression. Its proper determination appears to be key to the successful modelling of concrete under complex stresses. The aim of this paper is to clarify the e ff ect of ITZ cohesive parameters on predicted concrete behaviour, when the properties of the other constituents are determined by experiments. It is shown that the mortar plastic-damage behaviour has the strongest influence on the energy dissipation and overall stress-strain behaviour under both tension and compression. The e ff ect of ITZ parameters is limited to the post-peak softening branch and the crack patterns. Quasi-static experiments were carried out on mortar and concrete specimens: cylindrical specimens with diameter 100 mm and height 200 mm were tested in compression, dogbone specimens were tested in tension. Limestone aggregates with sieve size distribution between 6.3 and 10 mm were used for concrete samples. These were prepared with 40% aggregate volume fractions. Mortar specimens had the same water-cement-sand mixes as the ones used for concrete samples. Detailed experiment design will be presented elsewhere. 3D meso-structures were generated within prescribed volumes by random distribution of spherical aggregates with sizes selected from the sieve distribution and voids with 1% volume fraction. The generation used the ’take-and-place’ procedure described in detail in [8]. For this work, the meso-structures covered cylindrical volumes with diameter of 50 mm and height of 100 mm due to the computational cost if modelling the original cylinder. The same cylinders were adopted under tension, because direct tension test with cylinder was experimentally challenging and dogbone samples were applied for standard tension experiments. The volumes were tessellated into voxels in preparation for meshing used in image-based modelling. Voxel size of 0.25 mm was adopted after mesh sensitivity test. Tetrahedral meshes, covering aggregates and mortar phases were derived and an in-house procedure was used to insert zero-thickness cohesive elements (CE) at the aggregate-mortar interfaces to represent ITZ. The concrete-damage-plasticity (CDP) model is adopted for the constitutive law of mortar, because mortar can be considered as a lower-scale concrete. Under compression, the stress-strain response can be classified into four stages: linear elasticity, plasticity, strain hardening up to onset of damage and strain softening. The full expression is described by Equation (1) [9], where σ c and ε c are the current compressive stress and strain, respectively, σ c 0 and ε c 0 are the peak stress and corresponding strain, respectively, and ε cu is the strain at damage initiation, α a and α d are coe ffi cients related with σ cu . Under tension, the stress-strain relation is linear up to the peak stress, while the post peak behaviour can be expressed by Equation (2) [9], where α t is a coe ffi cient related with σ t 0 . 2. Experimental and modelling background

    E 0 ε c σ cu α a ε c ε cu α d

, σ c

0 . 4

σ c 0 ≤

+ (3 − 2 α a )

+ ( α a − 2)

ε c ε cu , ε c

ε c ε cu

2

3

, σ c

0 . 4 & ε c

1

σ c 0 ≥

ε cu ≤

σ c σ cu

(1)

=

ε c ε cu

1

ε cu ≥

1

2

ε c ε cu −

+ ε c ε cu